The numerical solution of partial differential-algebraic equations

Table 3 Comparison of the numerical solution of $u_{3} (x, t)$ with exact solutions ( $t = 0.01$ )

x	$u_{3} (x, t)$	$r_{4, 3} (x, t)$	$\| u_{3} (x, t) - r_{4, 3} (x, t) \|$
−0.5	0.002499958334	0.002499958333	1.10⁻¹²
−0.4	0.001599973333	0.001599973333	0
−0.3	0.0008999850001	0.0008999850000	1.10⁻¹³
−0.2	0.0003999933334	0.0003999933333	1.10⁻¹³
−0.1	0.00009999833334	0.00009999833333	1.10⁻¹⁴
0.1	0.00009999833334	0.00009999833333	1.10⁻¹⁴
0.2	0.0003999933334	0.0003999933333	1.10⁻¹³
0.3	0.0008999850001	0.0008999850000	1.10⁻¹³
0.4	0.001599973333	0.001599973333	0
0.5	0.002499958334	0.002499958333	1.10⁻¹²